wilcox.test              package:ctest              R Documentation

_W_i_l_c_o_x_o_n _R_a_n_k _S_u_m _a_n_d _S_i_g_n_e_d _R_a_n_k _T_e_s_t_s

_D_e_s_c_r_i_p_t_i_o_n:

     Performs one and two sample Wilcoxon tests on vectors of data.

_U_s_a_g_e:

     wilcox.test(x, ...)

     ## Default S3 method:
     wilcox.test(x, y = NULL, alternative = c("two.sided", "less", "greater"),
                 mu = 0, paired = FALSE, exact = NULL, correct = TRUE, 
                 conf.int = FALSE, conf.level = 0.95, ...)

     ## S3 method for class 'formula':
     wilcox.test(formula, data, subset, na.action, ...)

_A_r_g_u_m_e_n_t_s:

       x: numeric vector of data values.

       y: an optional numeric vector of data values.

alternative: a character string specifying the alternative hypothesis,
          must be one of '"two.sided"' (default), '"greater"' or
          '"less"'.  You can specify just the initial letter.

      mu: a number specifying an optional location parameter.

  paired: a logical indicating whether you want a paired test.

   exact: a logical indicating whether an exact p-value should be
          computed.

 correct: a logical indicating whether to apply continuity correction
          in the normal approximation for the p-value.

conf.int: a logical indicating whether a confidence interval should be
          computed.

conf.level: confidence level of the interval.

 formula: a formula of the form 'lhs ~ rhs' where 'lhs' is a numeric
          variable giving the data values and 'rhs' a factor with two
          levels giving the corresponding groups.

    data: an optional data frame containing the variables in the model
          formula.

  subset: an optional vector specifying a subset of observations to be
          used.

na.action: a function which indicates what should happen when the data
          contain 'NA's.  Defaults to 'getOption("na.action")'.

     ...: further arguments to be passed to or from methods.

_D_e_t_a_i_l_s:

     The formula interface is only applicable for the 2-sample tests.

     If only 'x' is given, or if both 'x' and 'y' are given and
     'paired' is 'TRUE', a Wilcoxon signed rank test of the null that
     the distribution of 'x' (in the one sample case) or of 'x-y' (in
     the paired two sample case) is symmetric about 'mu' is performed.

     Otherwise, if both 'x' and 'y' are given and 'paired' is 'FALSE',
     a Wilcoxon rank sum test (equivalent to the Mann-Whitney test) is
     carried out.  In this case, the null hypothesis is that the
     location of the distributions of 'x' and 'y' differ by 'mu'.

     By default (if 'exact' is not specified), an exact p-value is
     computed if the samples contain less than 50 finite values and
     there are no ties.  Otherwise, a normal approximation is used.

     Optionally (if argument 'conf.int' is true), a nonparametric
     confidence interval and an estimator for the pseudomedian
     (one-sample case) or for the difference of the location parameters
     'x-y' is computed.  (The pseudomedian of a distribution F is the
     median of the distribution of (u+v)/2, where u and v are
     independent, each with distribution F.  If F is symmetric, then
     the pseudomedian and median coincide.  See Hollander & Wolfe
     (1973), page 34.)  If exact p-values are available, an exact
     confidence interval is obtained by the algorithm described in
     Bauer (1972), and the Hodges-Lehmann estimator is employed. 
     Otherwise, the returned confidence interval and point estimate are
     based on normal approximations.

_V_a_l_u_e:

     A list with class '"htest"' containing the following components: 

statistic: the value of the test statistic with a name describing it.

parameter: the parameter(s) for the exact distribution of the test
          statistic.

 p.value: the p-value for the test.

null.value: the location parameter 'mu'.

alternative: a character string describing the alternative hypothesis.

  method: the type of test applied.

data.name: a character string giving the names of the data.

conf.int: a confidence interval for the location parameter. (Only
          present if argument 'conf.int = TRUE'.)

estimate: an estimate of the location parameter. (Only present if
          argument 'conf.int = TRUE'.)

_R_e_f_e_r_e_n_c_e_s:

     Myles Hollander & Douglas A. Wolfe (1973), _Nonparametric
     statistical inference_. New York: John Wiley & Sons. Pages 27-33
     (one-sample), 68-75 (two-sample).

     David F. Bauer (1972), Constructing confidence sets using rank
     statistics. _Journal of the American Statistical Association_
     *67*, 687-690.

_S_e_e _A_l_s_o:

     'kruskal.test' for testing homogeneity in location parameters in
     the case of two or more samples; 't.test' for a parametric
     alternative under normality assumptions.

_E_x_a_m_p_l_e_s:

     ## One-sample test.
     ## Hollander & Wolfe (1973), 29f.
     ## Hamilton depression scale factor measurements in 9 patients with
     ##  mixed anxiety and depression, taken at the first (x) and second
     ##  (y) visit after initiation of a therapy (administration of a
     ##  tranquilizer).
     x <- c(1.83,  0.50,  1.62,  2.48, 1.68, 1.88, 1.55, 3.06, 1.30)
     y <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29)
     wilcox.test(x, y, paired = TRUE, alternative = "greater")
     wilcox.test(y - x, alternative = "less")    # The same.
     wilcox.test(y - x, alternative = "less",
                 exact = FALSE, correct = FALSE) # H&W large sample
                                                 # approximation

     ## Two-sample test.
     ## Hollander & Wolfe (1973), 69f.
     ## Permeability constants of the human chorioamnion (a placental
     ##  membrane) at term (x) and between 12 to 26 weeks gestational
     ##  age (y).  The alternative of interest is greater permeability
     ##  of the human chorioamnion for the term pregnancy.
     x <- c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46)
     y <- c(1.15, 0.88, 0.90, 0.74, 1.21)
     wilcox.test(x, y, alternative = "g")        # greater
     wilcox.test(x, y, alternative = "greater",
                 exact = FALSE, correct = FALSE) # H&W large sample
                                                 # approximation

     wilcox.test(rnorm(10), rnorm(10, 2), conf.int = TRUE)

     ## Formula interface.
     data(airquality)
     boxplot(Ozone ~ Month, data = airquality)
     wilcox.test(Ozone ~ Month, data = airquality,
                 subset = Month %in% c(5, 8))

